Power spectrum estimation with missing values

In this paper, we consider estimation of a power spectrum from noise corrupted spectrum samples on uniform grids of frequencies with missing values. A scheme based on regularized nuclear norm optimization and subspace identification is proposed. The proposed scheme estimates model order and missing spectrum values in one step and is robust to large amplitude noise over short data records. Although this estimation problem can be cast as a spectrum estimation problem from non-uniformly spaced measurements and the algorithms developed for this type of data can be used, the identification example of this paper shows that the incomplete data formulation yields more accurate results.